Optimal Control of Multibody Systems

Analysis and application to Narrow Track Vehicles

Quentin Docquier


Tuesday, October 24, 2017, 11:00 - 12:00

Room 01-014, Georges-Köhler-Allee 103, Freiburg 79110, Germany

Optimal control is used in many fields to control dynamic systems. Among those, Multibody systems (MBS) entail strongly nonlinear dynamics and also imply constraints on both the state and the input of the system (e.g. actuator limits, safety operating conditions). In order to achieve online Model Predictive Control (MPC), fast solving of the OCP is required. Constrained multibody systems yield an index-3 DAE where the algebraic equations correspond to the holonomic constraints (e.g. loop closure). These equations can be written on different forms (implicit, semi-explicit or explicit in terms of the accelerations) and the index-3 of the DAE can be handled with different techniques. This work aims at analyzing which MBS formulation is the most suitable for Optimal Control. To do so, two scientific computer programs are interfaced: ROBOTRAN which provides symbolic expressions for the multibody dynamics and CASADI which formulates and solves the OCP. Results are presented showing the influence of the MBS formulations on the OCP solving (time, accuracy). Furthermore, fast MPC for MBS will be necessary for the active control of Narrow Track Vehicle. Because of their large height-to-track ratio, these vehicles need to be actively leaned toward the inside of a turn to prevent them from overturning in case of high-speed cornering. Two modes exist for active tilt control which are efficient in different speed ranges. The idea is to use Optimal Control to decide which control mode should be used in order to minimize the overall energy consumption and maximize comfort and handling for the driver.